Chapter 7 - Free vorticity shear layers and inverse methods

Summary

Introduction

So far we have considered only the case of fully attached inviscid steady flows, for which the introduction of a surface vorticity sheet of appropriate strength and of infinitesimal thickness, together with related trailing vorticity in three-dimensional flows, is completely adequate for a true representation. As pointed out in Chapter 1, where the justification of this model was argued from physical considerations, the surface vorticity method is representative of the infinite Reynolds number flow of a real fluid in all but one important respect, namely the problem of boundary layer separation. Real boundary layers involve complex mechanisms characterised by the influence of viscous shear stresses and vorticity convections and eddy formation on the free stream side. Depending upon the balance between these mechanisms and the consequent transfer of energy across a boundary layer, flow separation may occur when entering a rising pressure gradient, even at very high Reynolds numbers. Flow separation at a sharp corner will most certainly occur as in the case of flow past a flat plate held normal to the mainstream direction.

For a decade or so the development of computational fluid dynamic techniques to try to model these natural phenomena has attracted much attention and proceeded with remarkable success. The context of a good deal of this work has fallen rather more into the realm of classical methods than that of surface vorticity modelling, and is often classified by the generic title Vortex Dynamics.